A continuity result on quadratic matings with respect to parameters of odd denominator rationals

作者:Ma, Liangang*
来源:Mathematical Proceedings of the Cambridge Philosophical Society, 2019, 167(2): 369-388.
DOI:10.1017/S0305004118000397

摘要

In this paper we prove a continuity result on matings of quadratic lamination maps s(p) depending on odd denominator rationals p is an element of (0, 1). One of the two mating components is fixed in the result. Note that our result has its implication on continuity of matings of quadratic hyperbolic polynomials f(c)(z) = z(2) + c, c is an element of M the Mandelbrot set with respect to the usual parameters c. This is because every quadratic hyperbolic polynomial in M is contained in a bounded hyperbolic component. Its center is Thurston equivalent to some quadratic lamination map sp, and there are bounds on sizes of limbs of M and on sizes of limbs of the mating components on the quadratic parameter slice Per(m')(0).

  • 出版日期2019-9
  • 单位滨州学院

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